## Abstract

The κ-Clique problem is a fundamental combinatorial problem that plays a prominent role in classical as well as in parameterized complexity theory. It is among the most well-known NP-complete and W[1]-complete problems. Moreover, its average-case complexity analysis has created a long thread of research already since the 1970s. Here, we continue this line of research by studying the dependence of the average-case complexity of the κ-Clique problem on the parameter k. To this end, we define two natural parameterized analogs of efficient average-case algorithms. We then show that k-Clique admits both analogues for Erdős-Rényi random graphs of arbitrary density. We also show that κ-Clique is unlikely to admit either of these analogs for some specific computable input distribution.

Original language | English |
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Pages (from-to) | 18-29 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 576 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2015 |

## Keywords

- Average-case
- Clique
- Computational complexity
- Parameterized complexity

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science